Question

A die is rolled 100 times and the number appearing on the top face of the die is noted. The data is tabulated as follows:

Number	Frequency
1	20
2	10
3	20
4	30
5	10
6	10

Which of the following statements is/are true?

• A. P(Getting an odd number) = 0.5
• B. P(Getting a 2) = P(Getting a 3)
• C. P(Getting an even number) = 0.6
• D. P(Getting a 3) + P(Getting a 4) = 0.5

Answer 1

Answer: (A), (D)

The correct options are
A P(Getting an odd number) = 0.5
D P(Getting a 3) + P(Getting a 4) = 0.5

We know, for an event E,
$P\left(E\right)=\frac{\text{Number of trials in which the event happened}}{\text{Total number of trials}}$

So, probability of getting an odd number
$=\frac{Frequencyof1+Frequencyof3+Frequencyof5}{Totalnumberoftrials}=\frac{20+20+10}{100}=0.5$
$\therefore$ P(Getting an odd number) = 0.5

Also,
Probability of getting 2
$=\frac{Frequencyof2}{Totalnumberoftrials}=\frac{10}{100}=0.1$

Probability of getting 3
$=\frac{Frequencyof3}{Totalnumberoftrials}=\frac{20}{100}=0.2$
Hence, P(Getting a 2) is not equal to P(Getting a 3).

Also,
P(Getting an even number)
$=\frac{10+30+10}{100}=0.5$

We know, P(Getting a 3) = 0.2
P(Getting a 4) = $\frac{30}{100}$ = 0.3
$\therefore$ P(Getting a 3) + P(Getting a 4) = 0.2 + 0.3 = 0.5
Hence, P(Getting a 3) + P(Getting a 4) = 0.5